Some transportation problems and techniques for solving them

Abstract

AbstractThis article describes some transportation problems and presents algorithms for solving them. Except for the brief review of Network Flow Theory, which is used in developing the algorithm for the Fixed Resources‐Maximum Job Scheduling Problem, these are all scheduling problems.The Fixed Job–Minimum Resources Scheduling Problem presents a finite set of jobs, called sorties, to be done at given fixed times. The problem is to find, for vehicles of a given type, a schedule of greatest merit. One of the objectives involved in the definition of the merit function is that of minimizing the number of vehicles used.The Fixed Resources–Maximum Job Scheduling Problem is similar to the Fixed Job–Minimum Resources Scheduling Problem except that only a certain maximum number of vehicles maybe used, and the objective of minimizing the number of vehicles is replaced by the objective of maximizing the amount of work done. Also, in this section, it is shown that problems possessing certain symmetries are equivalent to simpler ones.The Slack Time–Fixed Job Scheduling Problem is somewhat analogous to the Fixed Job–Minimum Resources Scheduling Problem, and the Slack Time–Fixed Resources Scheduling Problem is somewhat analogous to the Fixed Resources, Maximum Job Scheduling Problem. The main difference is that instead of requiring that each sortie be performed at some given time, it is only required that it be performed within some given interval of time.The Slack Time–Fixed Job Scheduling and–Fixed Resources Scheduling Problems are more difficult to solve than the Fixed Job–Minimum Resources Scheduling and the Fixed Resources–Maximum Job Scheduling Problems. So in the Slack Time–Fixed Job Scheduling Problem a simplifying assumption is made concerning the times that it would take vehicles to return from destination points of sorties to the starting points of others. The method of solution presented for the Slack Time–Fixed Resources Scheduling Problem does not guarantee optimum solutions, but, it is hoped, good solutions. For a certain type of shuttling problem, it is proven that it does produce an optimum solution.